Home / DOE / Charts / Observed vs Predicted

Observed vs Predicted¶

This plot puts the response you measured on one axis and the value the model predicts for that same run on the other, one point per run, with a 45 degree reference line.

QXL DOE New > Charts > Regression Diagnostics > Observed vs Predicted

When to use it¶

A point sitting on the line means the model reproduced that run exactly. The scatter about the line is what the model failed to explain, so the plot shows how well the model fits across the whole range of the response in a single picture, and it shows where it fits worst.

Where the numbers come from¶

This chart is built from a regression sheet only. Design sheets are not offered, because the chart plots a value that only a fitted model can produce.

The predicted value is a fitted value, which only a model can produce, so there is no design sheet version of this chart.

Only a quantitative output is offered, as its Y-Hat or its S-Hat model. Binary and nominal outputs do not appear in the Outputs tree at all, so there is nothing to select and no message to read. A calibration plot for a logistic model, which is what the equivalent chart would be, is not built.

A chart built from a regression sheet does not re-fit the model. It reads the coefficients already on that sheet and evaluates the prediction equation with them.

Two things follow. The chart always agrees with the sheet it came from, so if you edit a coefficient the next chart changes with it. And a chart is only as current as its regression sheet: change the design and the old charts do not update, because nothing re-runs the regression for them.

The dialog¶

The left side of the dialog is a box headed Outputs holding a tree with three levels: the worksheet, then each output on it, then each level of that output. Tick the levels you want a chart for. The dialog opens with every level on the active sheet already ticked.

The two upper levels are three-state. Ticking a worksheet or an output ticks everything under it, and clearing it clears everything under it. When only some of the children are ticked, the parent shows a partial state rather than a tick, so the tree tells you at a glance whether a selection is complete.

One worksheet at a time. Ticking anything on a second worksheet silently clears every tick on the one you had selected, and the options on the right rebuild for the new sheet. There is no warning and no way to draw charts from two source sheets in one Create.

If you press Create with nothing ticked, the dialog tells you At least one chart must be selected. and stays open.

The options panel is a single box headed Observed vs Predicted. There are no axis, layout or set point controls, because both axes are fixed by what the chart is: the measured response against the fitted value, at the settings each run actually used.

This command writes its report in one step. There is no status line and no progress bar however many charts you asked for, and Cancel closes the dialog rather than stopping a run, because there is no between-chart point at which to stop.

What you get¶

All the plots you selected land on one worksheet called Observed vs Predicted, arranged in a grid, placed immediately to the right of the regression sheet. The heading line names the regression sheet the plots came from.

Each plot carries one point per used run and a 45 degree reference line. The two axes always share the same range and tick spacing, computed once over the combined observed and predicted values, even when the data would not require it. That is deliberate: a 45 degree line is only a fair reference when both axes are on the same scale, and the round tick spacing keeps the labels clean.

There is no confidence band. The reference line is the only annotation.

How it is calculated¶

The observed value is the response as entered on the design sheet for that run. The predicted value is the model evaluated at that run's own factor settings:

A prediction is the sum, over every term in the model, of that term's coded value times its coefficient:

\[ \hat{y} = \sum_{j} c_j \, b_j \]

where \(c_j\) is the coded value of term \(j\) at the settings you asked about and \(b_j\) is its coefficient from the regression table. The constant term has \(c_j = 1\), so its coefficient enters as itself.

A term that is absent from the regression table, or switched off for the level being predicted, contributes \(b_j = 0\).

There is no binary or nominal form of this chart, so the prediction here is always a value on the response scale rather than a probability. Full details: Prediction Equation.

Runs excluded from the regression are not plotted, so the point count matches the runs the model was actually fitted on rather than every row on the design sheet.